BS aside I would play mobile battle pets when away from the PC as a way to level them in game and such.
https://www.wowhead.com/title=340/khan
At your service
They don't need to link the AH directly to the Mobile game. They can have the Mobile game have its own AH market and own gold currency. However, they would/could allow you to purchase pets in-game in WoW, transfer to Mobile, and sell on their AH and such - and visa versa. yes, it of course effects the market... but you can already do that with Battle Pets and other servers via transferring pets from one server to another, since they're account-bound and not character-bound - and the server economies were fine.
And of course they would have players find a way to make Mobile-currency in the mobile game... probably thorough playing the game!? Ya think?! ;P
And, as you mentioned, they can always have that handy-dandy deplorable microtransaction "Pet-battle goldboost" option! ;P
Why would it cause outrage? You currently have a bunch of pets you can't obtain normally via microtransactions in the game. Nobody's screaming about that for the past several years...
Again, don't see the problem if the in-game mobile game has their own AH, and there would be plenty of WoW players trying to sell WoW-based pets on the mobile AH for mobile game currency if cross-play is allowed.
- - - Updated - - -
Ohhhhh, the old BG acheesement title. I thought that was some sort of internet slang like "Blursed" or something. :P
/raises hand here for "Seeker of Knowledge" title! ;P
there is a WoW game playable on phone, its called "Classic WoW"
100% I would play.